scholarly journals An optimization problem with volume constraint for a degenerate quasilinear operator

2006 ◽  
Vol 227 (1) ◽  
pp. 80-101 ◽  
Author(s):  
Julián Fernández Bonder ◽  
Sandra Martínez ◽  
Noemi Wolanski
Keyword(s):  
Optimization Problem ◽  
Volume Constraint ◽  
Quasilinear Operator

scholarly journals An optimization problem with volume constraint with applications to optimal mass transport

2019 ◽  
Vol 267 (10) ◽  
pp. 5870-5900
Author(s):  
João Vitor da Silva ◽  
Leandro M. Del Pezzo ◽  
Julio D. Rossi
Keyword(s):  
Mass Transport ◽  
Optimization Problem ◽  
Volume Constraint ◽  
Optimal Mass Transport

scholarly journals Finite element method for an eigenvalue optimization problem of the Schrödinger operator

2021 ◽  
Vol 7 (4) ◽  
pp. 5049-5071
Author(s):  
Shuangbing Guo ◽  
◽  
Xiliang Lu ◽  
Zhiyue Zhang ◽  
◽  
...  
Keyword(s):  
Finite Element ◽  
Schrödinger Operator ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Iteration Scheme ◽  
Schrodinger Operator ◽  
Volume Constraint ◽  
Eigenvalue Optimization ◽  
Finite Element Discretization ◽  
Element Discretization

<abstract><p>In this paper, we study the optimization algorithm to compute the smallest eigenvalue of the Schrödinger operator with volume constraint. A finite element discretization of this problem is established. We provide the error estimate for the numerical solution. The optimal solution can be approximated by a fixed point iteration scheme. Then a monotonic decreasing algorithm is presented to solve the eigenvalue optimization problem. Numerical simulations demonstrate the efficiency of the method.</p></abstract>

An Optimization Problem with Volume Constraint

1986 ◽  
Vol 24 (2) ◽  
pp. 191-198 ◽  
Author(s):  
N. Aguilera ◽  
H. W. Alt ◽  
L. A. Caffarelli
Keyword(s):  
Optimization Problem ◽  
Volume Constraint

scholarly journals Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations

2020 ◽  
Author(s):  
Idriss Mazari ◽  
Antoine Henrot ◽  
Yannick Privat
Keyword(s):  
Shape Optimization ◽  
Optimization Problem ◽  
Elliptic Partial Differential Equations ◽  
Volume Constraint ◽  
Standard Problem ◽  
Semilinear Elliptic ◽  
Dirichlet Type ◽  
Optimal Shapes ◽  
Linear Version ◽  
The Stability

Minimizing the so-called “Dirichlet energy” with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the problem, where one aims at mini- mizing a Dirichlet-type energy involving the solution to a semilinear elliptic PDE with respect to the domain, under a volume constraint. One of the main differences with the standard version of this problem rests upon the fact that the criterion to minimize does not write as the minimum of an energy, and thus most of the usual tools to analyze this problem cannot be used. By using a relaxed version of this problem, we first prove the existence of optimal shapes under several assumptions on the problem parameters. We then analyze the stability of the ball, expected to be a good candidate for solving the shape optimization problem, when the coefficients of the involved PDE are radially symmetric.

Exergy and sensibility analysis of each individual effect in a kraft multiple effect evaporator

TAPPI Journal ◽  
2019 ◽  
Vol 18 (10) ◽  
pp. 607-618
Author(s):  
JÉSSICA MOREIRA ◽  
BRUNO LACERDA DE OLIVEIRA CAMPOS ◽  
ESLY FERREIRA DA COSTA JUNIOR ◽  
ANDRÉA OLIVEIRA SOUZA DA COSTA
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Kraft Pulping ◽  
Steam Temperature ◽  
Input Flow ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Multiple Effect ◽  
Sensibility Analysis ◽  
Exergetic Analysis

The multiple effect evaporator (MEE) is an energy intensive step in the kraft pulping process. The exergetic analysis can be useful for locating irreversibilities in the process and pointing out which equipment is less efficient, and it could also be the object of optimization studies. In the present work, each evaporator of a real kraft system has been individually described using mass balance and thermodynamics principles (the first and the second laws). Real data from a kraft MEE were collected from a Brazilian plant and were used for the estimation of heat transfer coefficients in a nonlinear optimization problem, as well as for the validation of the model. An exergetic analysis was made for each effect individually, which resulted in effects 1A and 1B being the least efficient, and therefore having the greatest potential for improvement. A sensibility analysis was also performed, showing that steam temperature and liquor input flow rate are sensible parameters.

Imaging through Scattering Media with a Learning Based Prior

2020 ◽  
Vol 2020 (14) ◽  
pp. 306-1-306-6
Author(s):  
Florian Schiffers ◽  
Lionel Fiske ◽  
Pablo Ruiz ◽  
Aggelos K. Katsaggelos ◽  
Oliver Cossairt
Keyword(s):  
Optimization Problem ◽  
Autonomous Driving ◽  
Scattering Media ◽  
Photon Scattering ◽  
Point Spread ◽  
Spread Function ◽  
Radiative Transport Equation ◽  
Spatio Temporal ◽  
Transient Imaging

Imaging through scattering media finds applications in diverse fields from biomedicine to autonomous driving. However, interpreting the resulting images is difficult due to blur caused by the scattering of photons within the medium. Transient information, captured with fast temporal sensors, can be used to significantly improve the quality of images acquired in scattering conditions. Photon scattering, within a highly scattering media, is well modeled by the diffusion approximation of the Radiative Transport Equation (RTE). Its solution is easily derived which can be interpreted as a Spatio-Temporal Point Spread Function (STPSF). In this paper, we first discuss the properties of the ST-PSF and subsequently use this knowledge to simulate transient imaging through highly scattering media. We then propose a framework to invert the forward model, which assumes Poisson noise, to recover a noise-free, unblurred image by solving an optimization problem.

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